Binary digital phase shifters with phase increments of 360°/2n (referred to as “n-bit phase shifters”) are commonly used to scan a signal beam of a phased antenna array. Such digital phase shifters typically produce a “stair step” approximation to a desired linear phase gradient. A concern with such “stair step” approximations is that the stair stepping (e.g., jumping from one level to the next) can lead to significant errors in the desired scan angle of the signal beam. If the beam steering controller—the digital circuit that calculates the desired phase shifter settings for each element of the array—calculates high precision phase settings and then rounds the results to match the lower precision of the phase shifters, the beam pointing errors can be as high as the beamwidth/2n. For example, in an array with a 3-bit phase shifter, the error can be as high as one-eighth of a beamwidth.
Another concern is that “stair step” phase gradients that occur with digital phase shifters produce quantization sidelobes in the array patterns. A widely used equation to estimate the level of quantization sidelobes is n*6 dB, where “n” is the number of bits in the phase shifter (e.g., 18 dB for a 3-bit phase shifter.)
To achieve precision beam pointing, some designers have increased the complexity of the array by utilizing 4, 5 or 6 bit phase shifters. Additionally, to reduce aperture errors, several designers have either used or proposed using randomized round off, a control algorithm that involves a pseudo random number generator as a part of the round-off process in the beam steering controller circuits. Such a proportional randomization algorithm, however, is not repeatable. That is, if the same beam pointing command is sent to the beam steering and array repeatedly, each of the aperture phase settings will not be identical. This non-repeatable characteristic complicates checkout and testing of an antenna array.